Assignment question, root, Intermediate Value Theorem

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SUMMARY

The discussion centers on proving that the equation 3 arctan(2x-1) = cos²(x - (π/6)) + 1 has at least one positive real root using the Intermediate Value Theorem (IVT). The IVT states that if a continuous function changes signs over an interval, then there exists at least one root within that interval. The user expresses difficulty in understanding the problem due to recent ADHD diagnosis and medication, highlighting the need for clear guidance on applying the IVT to this specific equation.

PREREQUISITES
  • Understanding of the Intermediate Value Theorem (IVT)
  • Knowledge of trigonometric functions, specifically cosine and arctangent
  • Familiarity with continuous functions and their properties
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the application of the Intermediate Value Theorem in various mathematical contexts
  • Learn how to analyze the continuity of functions, particularly trigonometric and inverse trigonometric functions
  • Practice solving equations involving arctangent and cosine functions
  • Explore strategies for managing mathematical tasks with ADHD, including time management and focus techniques
USEFUL FOR

Students studying calculus, particularly those learning about the Intermediate Value Theorem, as well as individuals seeking strategies to overcome learning challenges such as ADHD in mathematical contexts.

kuttaman
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Homework Statement



Prove that Prove that the equation has at least one positive real root, using the Intermediate Value Theorem on an appropriate function.

3 arctan(2x-1)=cos^2(x-(∏/6)) + 1

Homework Equations



No clue

The Attempt at a Solution



I honestly speaking have no clue how to even start on this question, I have studied the text but my brain right now is just no functioning. I recently got diagnosed with ADHD and recentlyu started the medication (2days ago) so my head is a little sluggish and fatigued. Math is a bit of a thinking game, and this question is very detrimental for me to get. If someone can answer this/ or help me answer this it would be highly appreciated.
 
Last edited:
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kuttaman said:

Homework Statement



Prove that Prove that the equation has at least one positive real root, using the Intermediate Value Theorem on an appropriate function.

3 arctan(2x-1)=cos^2(x-(∏/6)) + 1

Homework Equations



No clue

The Attempt at a Solution



I honestly speaking have no clue how to even start on this question, I have studied the text but my brain right now is just not functioning. I recently got diagnosed with ADHD and recently started the medication (2days ago) so my head is a little sluggish and fatigued. Math is a bit of a thinking game, and this question is very detrimental for me to get. If someone can answer this/ or help me answer this it would be highly appreciated.
What does the Intermediate Value Theorem state ?
 

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